Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1997-12-01
Class.Quant.Grav. 15 (1998) 1767-1791
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
34 pages, plain LaTeX. Revisions: Two references added. Minor changes to the discussion of draining-bathtub geometries, and th
Scientific paper
10.1088/0264-9381/15/6/024
It is a deceptively simple question to ask how acoustic disturbances propagate in a non-homogeneous flowing fluid. This question can be answered by invoking the language of Lorentzian differential geometry: If the fluid is barotropic and inviscid, and the flow is irrotational (though possibly time dependent), then the equation of motion for the velocity potential describing a sound wave is identical to that for a minimally coupled massless scalar field propagating in a (3+1)-dimensional Lorentzian geometry. The acoustic metric governing the propagation of sound depends algebraically on the density, flow velocity, and local speed of sound. This rather simple physical system is the basis underlying a deep and fruitful analogy between the black holes of Einstein gravity and supersonic fluid flows. Many results and definitions can be carried over directly from one system to another. For example, I will show how to define the ergosphere, trapped regions, acoustic apparent horizon, and acoustic event horizon for a supersonic fluid flow, and will exhibit the close relationship between the acoustic metric for the fluid flow surrounding a point sink and the Painleve-Gullstrand form of the Schwarzschild metric for a black hole. This analysis can be used either to provide a concrete non-relativistic model for black hole physics, up to and including Hawking radiation, or to provide a framework for attacking acoustics problems with the full power of Lorentzian differential geometry.
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